Determine the functions if they are inverse of each other by composite method:
[tex]\begin{gathered} f(x)=\frac{1}{x^3}+3 \\ g(x)=\sqrt[3]{\frac{1}{x-3}} \end{gathered}[/tex][tex]\begin{gathered} \mathrm{A\: function\: g\: is\: the\: inverse\: of\: function\: f\: if\: for}\: y=f\mleft(x\mright),\: \: x=g\mleft(y\mright) \\ y=\frac{1}{x^3}+3 \\ \text{replace x with y} \end{gathered}[/tex][tex]undefined[/tex]
Hence the functions are inverse of each other
Therefore the correct answer is Yes
